A planar current loop consists of two semicircular arcs carrying current I = 12 A, with radii R₁ = 6π m and R₂ = 4π m, joined by radial straight segments as shown in the original figure. If the net magnetic field at the common centre O is k×10⁻⁷ T, find k. Take μ₀ = 4π×10⁻⁷ T m A⁻¹.

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G1 Physics · Accepted Answer

The radial straight segments produce zero magnetic field at O because for every current element on those segments, dl is parallel to the position vector toward O. Magnetic field at the centre of a semicircle is B = μ₀I/(4R). For R₁ = 6π m: B₁ = (4π×10⁻⁷)(12)/[4(6π)] = 2×10⁻⁷ T. For R₂ = 4π m: B₂ = (4π×10⁻⁷)(12)/[4(4π)] = 3×10⁻⁷ T. The two semicircular arcs carry current around O in opposite senses, so their fields oppose. Thus, B n e t B_net B n ​ e t = B₂-B₁ = (3-2)×10⁻⁷ = 1×10⁻⁷ T. Hence k =…